KANSAS CITY, Mo. — His voice quivering, his eyes red, Royals closer Kelvin Herrera walked into a foyer outside the Kauffman Stadium press box at just past 7:50 p.m. Monday. He wore jeans, a dark shirt and a black hat. As he turned toward a Royals official, he took a deep breath. After eight years in Kansas City, he prepared to say goodbye.

“This is a moment that I was not expecting,” Herrera said.

On the third Monday in June, the Royals’ expected fire sale pressed on, the club sending Herrera, 28, to the Washington Nationals for minor-league infielder Kelvin Gutierrez, outfielder Blake Perkins and right-handed pitcher Yohanse Morel. In a move that further signaled the club’s desire to be aggressive this summer, the only surprise concerned the timing.

Royals general manager Dayton Moore called Herrera “simply family.” Herrera thanked the organization and the city he came to love. Yet as both men grappled with the emotions of the moment, one thing...